Well first you would like to get like variables on each side for just one variable. for example:
2x + 3y = 10 and x - y = 5
You would change the x - y so that way the x variable would be isolated:
x = 5 + y
Now you must substitute the 5 + y into the other equation for x:
2(5 + y) + 3y = 10
10 + 2y + 3y = 10
Combine like terms 5y + 10 = 10
In this case it would be insolvable because it would change to 5y = 0
So let's try the other equation.
2x + 3y = 10
5y = 10
y = 2
Now substitute this into the other equation:
x - 2 = 5
x = 7
There is your two answers.
x = 7 and y = 2